Studies in Numerical Nonlinear Instability III: Augmented Hamiltonian Systems

DOI10.1137/0147005zbMath0632.65129OpenAlexW1965002511MaRDI QIDQ3769925

Fernando Vadillo, Jesús María Sanz-Serna

Publication date: 1987

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0147005

zbMATH Keywords

dynamical systemsHamiltonian systemscubic Schrödinger equationnonlinear instabilityKolmogorov-Arnold-Moser theoryleapfrog discretizations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (9)

Studies in numerical nonlinear instability. II. A new look at \(u_ t+uu_ x=0\) ⋮ Runge-Kutta schemes for Hamiltonian systems ⋮ Split-step spectral schemes for nonlinear Dirac systems ⋮ An iterative starting method to control parasitism for the Leapfrog method ⋮ Exact analysis of nonlinear instability in a discrete Burgers' equation ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods ⋮ Symplectic Runge-Kutta and related methods: Recent results ⋮ An easily implementable fourth-order method for the time integration of wave problems ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods

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